Important Formulas for CAT 2020 Preparation - CAT Exam Revision Tips

Important Formulas for CAT Preparation - Proceeding further towards CAT important formulas, lets get familiar with the “Importance of CAT Formulas”. When it comes to CAT preparation basically for the Quantitative Aptitude section, the most important aspect is remembering the formulas and theorems and by knowing such key formulas one will get to know when and how to apply them. Thus, it becomes more important that a candidate will have to be well versed with the basic formulas as it is required to solve the questions with good speed and accuracy rate. The questions in the QA section are from various topics such as Profit, Loss and Discount, Number System, Time and Work, LCM and HCF, Logarithm, Averages, Set theory & Function, Probability, Permutation & Combination, Trigonometry, Mensuration, Coordinate Geometry, etc. Formulae are the basic and indispensable part to ace the quantitative section in the CAT. They may be proved to be an elixir to the section, if one does their preparation in an appropriate manner. So as one starts their CAT 2020 preparation, here is the list of important formulae that one needs to master to crack the Common Admission Test successfully.
Latest: CAT 2020 registration date extended to September 23. IIM Indore has made changes in CAT 2020 exam pattern.

CAT 2020 Basic Mathematical Formulas

• (a + b)² = (a² + b² + 2ab)

• (a – b)² = (a² + b² – 2ab)

• (a + b)(a – b) = (a² – b²)

• (a + b)² = (a² + b² + 2ab)

• (a³ – b³) = (a – b)(a² + ab + b²)

• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

• (a³ + b³) = (a + b)(a² – ab + b²)

• When a + b + c = 0, then a³ + b³ + c³ = 3abc

• (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)

• (a + b)n = an + (nC1)an-1b + (nC2)an-2b² + … + (nCn-1)abn-1 + bn

CAT Important Formulas for Number System

• (1² + 2² + 3² + ….. + n²) = n ( n + 1 ) (2n + 1) / 6

• 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2

• (1³ + 2³ + 3³ + ….. + n³) = (n(n + 1)/ 2)²

• Sum of first n odd numbers = n²

• Sum of first n even numbers = n (n + 1)

Formulas for LCM and HCF

• LCM × HCF = Product of the Numbers

• LCM of Co-prime Numbers = Product Of The Numbers

Mathematical Formulas for Profit, Loss and Discount

• Profit % = Profit/(C P)×100

• Profit/Gain = (S.P.) – (C.P.)

• C P = 100/(100+gain %)×S P

• S P = (100+gain % )/100 ×C P

• Loss % = Loss/(C.P.)×100

• Loss = (C.P.) – (S.P.)

• C P = 100/(100-loss %)×S P

• S P = (100-loss %)/100×C P

Formulae for Percentages

Find what percentage of X is Y: Y/X x 100

• Increase N by S% = N(1+S/100)

• Decrease N by S% = N(1 - S/100)

Important Formulas for Speed, Time and Distance

• Speed= Distance/ Time

• Distance= Speed x Time

• Time= Distance/ Time

Time and Work Formulas (Basic Formulas)

• If X can do a piece of work in ‘n’ days, then X’s 1 day’s work= 1/n

• If X’s 1 day’s work= 1/n, then X can finish the work in n days.

Averages Formula

Average= Sum of observations/ Number of observations

Simple and Compound Interest Formula

• Simple Interest: P x i x n (P= Principle, i= interest rate and n= term of the loan)

• Compound Interest:

  • Compound Interest = [P(1+i)n] - P

  • Compound Interest = P[(1+i)n-1]

Mathematical Logarithm Formulas

• If n and a are positive real numbers, and a is not equal to 1, then If ax = n, then log a n = x

• log of 1 to any base is 0 (log b 1 = 0)

• log of any number to base as itself is 1, log a a = 1

• Logarithm of a Product (log a pq = log a p + loga q)

• Logarithm of a Fraction (log a (p/q) = log a p – log a q)

• log a pn = n log a p

• a(log a p) = p

• Base Change Rule of Logarithms: (log a n = log b n × log a b)

CAT 2020 Trigonometry Formulas

• Trigonometric Identities

  • Sine=Opposite/Hypotenuse

  • Secant=Hypotenuse/Adjacent

  • Cosine=Adjacent/Hypotenuse

  • Tangent=Opposite/Adjacent

  • Co−Secant=Hypotenuse/Opposite

  • Co−Tangent=Adjacent/Opposite

• The reciprocal identities are given as

  • CosecΘ=1/sinΘ

  • secΘ=1/cosΘ

  • cotΘ=1/tanΘ

  • sinΘ=1/CosecΘ

  • cosΘ=1/secΘ

  • tanΘ=1/cotΘ

Mathematical Mensuration Formulas

• Rectangle

  • Area = lb

  • Perimeter = 2(l+b)

• Square

  • Perimeter = 4a

  • Area = a×a

• Triangle

  • Area =b×h/2 or √s(s-a)(s-b)(s-c)…………….where s=a+b+c/2

• Cube

  • Volume: V = l3

  • Surface Area: S = 6s2

  • Diagonal (d) = √3l

  • Lateral surface area = 4a2

• Circle

  • Circumference = 2πr or πd

  • Area = πr² or πd²/4

  • Area of sector of a circle = (θπr² )/360

• Cuboid

  • Total surface area = 2 (lb + bh + hl) or 6l2

  • Volume of cuboid: lbh

  • Length of diagonal =√(l²+b²+h²)

Formulas for Coordinate Geometry

• AB² = (Bx – Ax)² + (By – Ay)²

• Midpoint of the line joining the points (x1, y1) and (x2, y2) is:

  • [½(x1 + x2), ½(y1 + y2)]

CAT 2020 Formulas for Surds and Indices

Mixtures and Allegation Formula

If 2 ingredients are mixed, then

• (Quantity of cheaper/ Quantity of dearer) = (C.P of dearer - Mean price/ Mean price - C.P of cheaper)

Permutation and Combination Formula for CAT 2020

• Permutation Formula

• Combination Formula

Formulas for Set Theory and Function

• (A ∩ B) ‘ = A’ U B’ and (A U B)’ = A’ ∩ B’